Estimation of regional flows by signals detected externally is done from transit time estimations; when the input is an impulse or the transit time is long compared to the duration of the input model free techniques work well, unless recirculation occurs. When the marker is restricted to the intravascular or extracellular spaces the mean transit time is short and recirculated tracer is in higher concentration. Partial barrier limitation to transport complicates the shapes of the curves. The goal of this project is to develop general approaches to flow estimation for X-ray CT, NMR, ultrasonic and PET methods of detection using indicators which suffer from these types of difficulties.